# Particle / Anti-particle Annihilations

Are there any experimental or theoretical limits on the distance at which a particle / anti-particle pair ( or pair for short ) can annihilate? If there is, are there any limits on the duration a pair must be within said distance in order for an annihilation to occur?

In other words: Do there exist, at the very least theoretical, conditions under which a colocated ( read: very close ) pair can be guaranteed to seperate fast enough to "escape annihilation" ?

I realize this question relies on a great deal more than the simple notions of distance, time and motion, so any reference material would be greatly appreciated.

-joeboo

## Answers and Replies

jtbell
Mentor
At the quantum-mechanical level, physicists don't think in terms of distance of closest approach, because you can't think of either particle as having a definite position at any particular time. (Remember the Heisenberg Uncertainty Principle?)

Instead, we think in probabilistic terms, using a quantity called the interaction cross section. If we have a thin target of thickness $dx$, containing $n$ electrons per m^3, and we fire $N_0$ positrons at it, the number $dN$ that annihilate is, on the average,

$$dN = \sigma N_0 n dx$$

where the proportionality constant $\sigma$ is the interaction cross section for annihilation. We can measure $\sigma$ by counting how many positrons actually annihilate, and calculating

$$\sigma = \frac {1}{N_0 n} \frac {dN}{dx}$$

We can also predict $\sigma$ from theory, using quantum electrodynamics. It depends on the energy of the positrons.

A Google search on

electron positron annihilation cross section

turns up a lot of pages, some of which have theoretically-derived formulas for $\sigma$, and others which have the measured values.